How does the spatial process change with:
source: airnow.gov
To rewrite the constrained optimization in terms of \(l_i\) we get \[-\sum_{i=0}^n \sum_{j=0}^n a_i a_j \gamma(\boldsymbol{s_i} - \boldsymbol{s_j}) = -\sum_{i=1}^n \sum_{j=1}^n l_i l_j \gamma_{ij} + 2 \sum_{i=1}^n l_i \gamma_{0i},\] where \(\gamma_{ij} = \gamma(\boldsymbol{s}_i - \boldsymbol{s}_j)\) and hence \(\gamma_{0j} = \gamma(\boldsymbol{s}_0 - \boldsymbol{s}_j)\)
Consider a small example on 1-dimension.
What should the predictions be at \(\boldsymbol{s}^{*}_1 = 4\) and \(\boldsymbol{s}^{*}_2 = 6\)
Define \(\gamma(h) = 1 - \exp(- \frac{h}{3})\) and compute the BLUPs for \(\boldsymbol{s}_1^{*}\) and \(\boldsymbol{s}_2^{*}\)
Interpret and explain \(\boldsymbol{l}\) for each sample point.
If you have time, fill in the line (rather than the surface) from (0.5, 7.5)